Certified bottleneck transitions and balanced capacity upgrades in robust production–distribution networks

Manufacturing resources and shipping routes can constrain the same customer commitment, making both uncertainty audits and capacity spending sensitive to changing bottlenecks. This paper develops a certified production–distribution analysis under a static uncertainty model with common resource-coefficient inflation. A reparameterization converts the uncertainty path to a fixed-matrix LP and yields a finite dual-line envelope for maximal supportable commitment stress. A certificate-driven interval procedure traces transitions with explicit upper and lower bounds. A budgeted resource–route upgrade model then derives marginal budget value by minimizing the largest price-normalized multiplier over the entire baseline-optimal dual face. A family with \(k\) simultaneous bottlenecks shows that an arbitrary extreme certificate can overstate marginal value by a factor \(k\), while upgrading only its indicated bottleneck produces zero gain. An explicit two-plant family provides an exact switching law and constructive shipment proof. Computation covers 36 networks with up to 144 shipment variables, 180 budgeted upgrade cases and 25 serial-bottleneck cases. Independently solved primal and dual programs verify the envelope and spending calculations. The method specializes established LP and parametric-optimization principles; its contribution is the linked bottleneck-and-upgrade audit with explicit failure families. All experiments are synthetic.